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Population Simulation Using MatLab

Population Simulation Using MatLab. Jie Ma EPS 109 Professor. Militzer. Fox vs. Rabbit. 1. Predator-prey Function: (Lab3) Predator : Fox Prey : Rabbit 2. Solve Differential Equation (Lab 13) Runge Kutta Method Stable when dx/ dt = 0; dr / dt = 0;. Population changes .

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Population Simulation Using MatLab

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  1. Population Simulation Using MatLab Jie Ma EPS 109 Professor. Militzer

  2. Fox vs. Rabbit • 1. Predator-prey Function: (Lab3) • Predator: Fox • Prey: Rabbit • 2. Solve Differential Equation (Lab 13) • RungeKutta Method • Stable when dx/dt = 0; dr/ dt = 0;

  3. Population changes How to visualize? Red: Fox Blue: rabbit Reference the Random walk Lab5: Generate a white matrix to represent the total population Using Red grad to represent fox population and blue grad to represent the rabbit population Use random number to generate a random location of Fox or Rabbit.

  4. Red for Fox and Blue for rabbit • When the rabbit population increase, the fox population increase, and rabbit population decrease. for j = 1:numFox %calculte the index of the location while 1 randloc = round(rand()*maxPoP); rand_row = round(mod(randloc,sn))+1; rand_col = round(randloc/sn)+1; %if the poistion has already be not been taken, reject to move if(A(rand_row,rand_col,2) == 255) A(rand_row,rand_col,1) = 255; A(rand_row,rand_col,2) = 0; A(rand_row,rand_col,3) = 0; break end end end

  5. Peppered Moth evolution X for bird: dx/dt= (-d +e * y+ et *z) * x; Y for White Moth: dy/dt= (kr*( m –y )- c * x) *y; Z for Bluemoth: dz/dt= (kt*(mt- z)-ct* x )* z; C > Ct

  6. Background color : gray Yellow: white peppered moth Black: black peppered moth • Their dark color blend them in the polluted trees and makes it • difficult to find by their predators. As a result they are more likely to • survive and reproduce. As a result, the black moth population increase.

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